Quantitative Biology
ISBN: 9780262364409  Copyright 0
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Contents (pg. vii)  
1. Introduction to Quantitative Biology (pg. 1)  
1.1 History and Overview of the qbio Summer School (pg. 1)  
1.2 Origin and Organization of this Textbook (pg. 2)  
1.3 How to Use this Book (pg. 4)  
1.4 Acknowledgments (pg. 6)  
2. Fostering Collaborations between Experimentalists and Modelers (pg. 9)  
2.1 Education (pg. 10)  
2.2 Presentation (pg. 10)  
2.3 Practice (pg. 11)  
2.4 Attitude (pg. 11)  
I. Defining and Simulating Models (pg. 13)  
Introduction to the Simulation of Models (pg. 15)  
3. Modeling with Ordinary Differential Equations (pg. 19)  
3.1 Introduction (pg. 19)  
3.2 A Primer to Ordinary Differential Equations (pg. 20)  
3.3 From Biochemical Reactions Networks to ODEs (pg. 21)  
3.4 Solving ODEs (pg. 27)  
3.5 Complex Dynamic Behavior: Different Types of Solutions (pg. 33)  
3.6 Detailed Balance: Thermodynamic Constraints (pg. 36)  
3.7 Model Simplifications and Level of Abstraction (pg. 38)  
3.8 Some Advanced Modeling Concepts (pg. 42)  
3.9 Overview of Relevant Software Tools (pg. 45)  
3.10 Exercises (pg. 46)  
4. Modeling with Partial Differential Equations (pg. 49)  
4.1 Introduction to Partial Differential Equations (pg. 49)  
4.2 PDE Theory (pg. 56)  
4.3 Analytical Solutions (pg. 57)  
4.4 Numerical Solutions (pg. 63)  
4.5 Summary and Discussion (pg. 66)  
4.6 Exercises (pg. 66)  
5. Stochasticity or Noise in Biochemical Reactions (pg. 71)  
5.1 Introduction (pg. 71)  
5.2 The Chemical Master Equation (pg. 73)  
5.3 Analyzing Population Statistics with FSP Approaches (pg. 77)  
5.4 Comparing CME Models to SingleCell Data (pg. 83)  
5.5 Examples (pg. 85)  
5.6 Summary (pg. 91)  
5.7 Exercises (pg. 92)  
6. The LinearNoise Approximation and Moment Closure Approximations for Stochastic Chemical Kinetics (pg. 95)  
6.1 Introduction (pg. 95)  
6.2 Stochastic Models of Biochemical Systems (pg. 96)  
6.3 Time Evolution of Statistical Moments (pg. 98)  
6.4 Moment Closure Methods (pg. 101)  
6.5 The LinearNoise Approximation (pg. 105)  
6.6 Conclusion (pg. 111)  
6.7 Exercises (pg. 112)  
7. Kinetic Monte Carlo Analyses of Discrete Biomolecular Events (pg. 113)  
7.1 Introduction to Stochastic Simulations (pg. 113)  
7.2 Example (pg. 127)  
7.3 Model Specification Using Petri Nets (pg. 128)  
7.4 bioPN (pg. 131)  
7.5 Exercises (pg. 135)  
8. The Extra Reaction Algorithm for Stochastic Simulation of Biochemical Reaction Systems in Fluctuating Environments (pg. 137)  
8.1 Introduction (pg. 137)  
8.2 The Extrande Method (pg. 138)  
8.3 Gene Expression with TimeVarying Transcription (pg. 142)  
8.4 Discussion (pg. 145)  
9. SpatialStochastic Simulation of ReactionDiffusion Systems (pg. 149)  
9.1 Why Spatiality Matters (pg. 150)  
9.2 Brownian Dynamics Simulations with Reactions (pg. 152)  
9.3 EventDriven Schemes (pg. 161)  
9.4 Recent Developments: Hybrid Schemes and Parallelization (pg. 172)  
9.5 Further Reading (pg. 173)  
9.6 Online Resources (pg. 173)  
9.7 Summary (pg. 174)  
9.8 Exercises (pg. 174)  
10. Introduction to Molecular Simulation (pg. 179)  
10.1 Introduction (pg. 179)  
10.2 Molecular Dynamics (pg. 180)  
10.3 Monte Carlo Sampling (pg. 185)  
10.4 Practical Aspects of Numerical Simulations (pg. 187)  
10.5 Acceleration of Equilibration and Simulating Rare Events (pg. 195)  
10.6 Simulation Tools (pg. 199)  
10.7 Summary (pg. 202)  
10.8 Exercises (pg. 203)  
II. Model Development and Analysis Tools (pg. 207)  
Introduction to Model Development and Analysis (pg. 209)  
11. ReverseEngineering Biological Networks from Large Data Sets (pg. 213)  
11.1 Lay of the Land (pg. 213)  
11.2 Roles for ReverseEngineering in Systems Biology Research (pg. 220)  
11.3 Two Different Meanings of Phenomenological "Reconstruction'' (pg. 228)  
11.4 Discussion (pg. 241)  
11.5 Try on Your Own: Become a Reverse Engineer (pg. 244)  
11.6 Exercises (pg. 245)  
12. Mathematically Controlled Comparisons for Elucidation of Biological Design Principles (pg. 247)  
12.1 Introduction (pg. 248)  
12.2 EndProduct Inhibition: SteadyState Behavior (pg. 251)  
12.3 Transcriptional Autorepression: Dynamic Behavior (pg. 259)  
12.4 Discussion (pg. 265)  
12.5 Summary (pg. 268)  
12.6 Exercises (pg. 269)  
13. Parameter Estimation, Sloppiness, and Model Identifiability (pg. 271)  
13.1 Introduction (pg. 272)  
13.2 Formulating the Parameter Estimation Problem (pg. 273)  
13.3 Solving the Inverse Problem: Nonlinear Optimization (pg. 277)  
13.4 Model Identifiability: Parameters Cannot Always Be Estimated (pg. 279)  
13.5 Precision of Parameter Estimates Using Sensitivity Analysis (pg. 283)  
13.6 Parameter Estimation in the Wild: Practicalities (pg. 289)  
13.7 Summary (pg. 290)  
13.8 Exercises (pg. 290)  
14. Sensitivity Analysis (pg. 293)  
14.1 Introduction (pg. 293)  
14.2 Theoretical Concepts (pg. 294)  
14.3 Applications of the Sensitivity Analysis (pg. 305)  
14.4 Summary (pg. 315)  
14.5 Exercises (pg. 316)  
15. Experimental Design (pg. 321)  
15.1 Introduction (pg. 321)  
15.2 General Framework (pg. 322)  
15.3 Frequentist Approach (pg. 323)  
15.4 Bayesian Approach (pg. 326)  
15.5 Asymptotic Equivalency (pg. 327)  
15.6 Applications of Experiment Design (pg. 328)  
15.7 Discussion (pg. 334)  
15.8 Exercises (pg. 335)  
16. Bayesian Parameter Estimation and Markov Chain Monte Carlo (pg. 339)  
16.1 Introduction (pg. 339)  
16.2 LikelihoodBased Inference (pg. 340)  
16.3 Bayesian Inference (pg. 343)  
16.4 Markov Chain Monte Carlo for Bayesian Inference (pg. 345)  
16.5 LikelihoodFree Methods for Bayesian Inference (pg. 350)  
16.6 Exercises (pg. 355)  
17. Uses of Bifurcation Analysis in Understanding Cellular DecisionMaking Dongya Jia, Mohit Kumar Jolly, and Herbert Levine (pg. 357)  
17.1 Introduction (pg. 357)  
17.2 Basic Concepts in Bifurcation Analysis (pg. 360)  
17.3 Bifurcations in One Dimension (pg. 363)  
17.4 Using Bifurcation Theory to Understand Cellular DecisionMaking (pg. 365)  
17.5 Bifurcation Theory in Parameter Sensitivity Analyses (pg. 375)  
17.6 Bifurcation Theory and Experimental Testing with Flow Cytometry (pg. 377)  
17.7 Conclusions (pg. 377)  
17.8 Exercises (pg. 378)  
18. Performance Measures for Stochastic Processes and the MatrixAnalytic Approach (pg. 379)  
18.1 Introduction (pg. 379)  
18.2 Analysis of the Stochastic Descriptors: An Application to VEGFR2/VEGFA Interaction and Signaling (pg. 382)  
18.3 Numerical Results (pg. 392)  
18.4 Discussion (pg. 394)  
III. Modeling in Practice (pg. 401)  
Introduction to Computational Modeling Tools in Quantitative Biology (pg. 403)  
19. Setting Up and Simulating ODE Models (pg. 405)  
19.1 Introduction to Tellurium: A PythonBased Platform (pg. 405)  
19.2 Building and Simulating a Model (pg. 406)  
19.3 Antimony: Network Description Language (pg. 409)  
19.4 Running Simulations (pg. 411)  
19.5 Fitting Models to Data (pg. 413)  
19.6 Validation, Validation, and More Validation (pg. 416)  
19.7 Publishing a Reproducible Model (pg. 418)  
19.8 Illustrative Examples (pg. 420)  
19.9 Summary (pg. 421)  
19.10 Availability of Software (pg. 421)  
19.11 Exercises (pg. 421)  
20. Accelerating Stochastic Simulations Using Graphics Processing Units (pg. 423)  
20.1 Introduction (pg. 423)  
20.2 Methods (pg. 426)  
20.3 Example (pg. 437)  
20.4 Discussion (pg. 440)  
21. RuleBased Modeling Using Virtual Cell (VCELL) (pg. 441)  
21.1 Introduction (pg. 441)  
21.2 RuleBased Modeling in VCell (pg. 444)  
21.3 Physiology (pg. 445)  
21.4 RuleBased Modeling in VCell: Applications and Simulations (pg. 451)  
21.5 Conclusions (pg. 453)  
21.6 Additional Information (pg. 454)  
22. Spatial Modeling of Cellular Systems with VCELL (pg. 455)  
22.1 Introduction (pg. 455)  
22.2 Compartmental Models: Sizes of Cellular Compartments May Matter even if Diffusion is Fast on the Time Scale of Reactions (pg. 456)  
22.3 ReactionDiffusion in Explicit Geometries: Why Space Should Be Explicitly Modeled (pg. 459)  
22.4 Numerical Approaches to Spatial Models Arising in Cell Biology (pg. 462)  
22.5 Conclusion (pg. 468)  
23. Stochastic Simulation of WellMixed and Spatially Inhomogeneous Biochemical Systems (pg. 469)  
23.1 Introduction (pg. 469)  
23.2 Algorithms (pg. 471)  
23.3 Software for Stochastic Simulation of Biochemical Systems (pg. 474)  
23.4 Examples (pg. 477)  
23.5 Discussion (pg. 480)  
23.6 Summary (pg. 483)  
23.7 Exercises (pg. 483)  
24. Spatial Stochastic Modeling with MCell and CellBlender (pg. 485)  
24.1 Introduction: Why Stochastic Spatial Modeling? (pg. 485)  
24.2 A Brief Overview of MCell (pg. 488)  
24.3 Getting Started with CellBlender and MCell (pg. 493)  
24.4 Simulating Free Molecular Diffusion (pg. 495)  
24.5 Restricting Diffusion by Defining Meshes (pg. 497)  
24.6 Simulating Bimolecular Reactions in a Volume (pg. 499)  
24.7 Simulating Molecules and Reactions on Surfaces (pg. 504)  
24.8 Extended Exercise: A DensityDependent Switch (pg. 509)  
24.9 Concluding Remarks (pg. 511)  
IV. Example Models and Specialized Methods (pg. 513)  
Introduction to Examples in Quantitative Biology (pg. 515)  
25. The Use of Linear Analysis and Sensitivity Functions in Exploring TradeOffs in Biology: Applications to Glycolytic Oscillations (pg. 519)  
25.1 Introduction (pg. 519)  
25.2 Analysis of the Minimal Model of Glycolysis (pg. 524)  
25.3 Discussion (pg. 528)  
26. Models of Bacterial Chemotaxis (pg. 531)  
26.1 Introduction: The E. coli Chemotaxis Network (pg. 531)  
26.2 IsingType Description of the E. coli Chemotactic Process (pg. 536)  
26.3 Summary (pg. 544)  
27. Modeling Viral Dynamics (pg. 545)  
27.1 Introduction: Basic Biology of HIV Infection (pg. 546)  
27.2 A Simple Model of HIV Dynamics (pg. 547)  
27.3 Basic Principles of Viral Dynamics and Drug Treatment (pg. 549)  
27.4 Using Modeling to Gain Further Insight into HIV1 Biology (pg. 551)  
27.5 Other Model Applications and Extensions (pg. 557)  
27.6 Further Reading (pg. 561)  
27.7 Exercises (pg. 561)  
28. Stochastic Modeling of Gene Expression, Protein Modification, and Polymerization (pg. 563)  
28.1 Introduction (pg. 563)  
28.2 Gene Expression (pg. 564)  
28.3 Protein Modification (pg. 572)  
28.4 Polymerization (pg. 574)  
28.5 Interactions (pg. 577)  
28.6 More Complex Phenomena (pg. 579)  
28.7 Summary and Outlook (pg. 580)  
28.8 Exercises (pg. 580)  
29. Modeling CellFate Decisions in Biological Systems: Bacteriophage, Hematopoietic Stem Cells, EpithelialtoMesenchymal Transition, and Beyond (pg. 583)  
29.1 Introduction (pg. 583)  
29.2 Lysis/Lysogeny Decision in Lambda Phage (pg. 585)  
29.3 CellFate Decisions in Hematopoietic Stem Cell System (pg. 588)  
29.4 EpithelialtoMesenchymal Transition (pg. 590)  
29.5 NotchDeltaJagged Signaling (pg. 594)  
29.6 Which Modeling Framework to Use and When? (pg. 597)  
29.7 Exercises (pg. 598)  
30. Tutorial on the Identification of Gene Regulation Models from SingleCell Data (pg. 599)  
30.1 Outline of Our Approach (pg. 599)  
30.2 Gene Regulation Model Description (pg. 600)  
30.3 Exercise Tasks (pg. 603)  
30.4 Exercise Results and GUI (pg. 614)  
30.5 Summary and Conclusions (pg. 616)  
References (pg. 617)  
Contributors (pg. 695)  
Index (pg. 701)  
Contents (pg. vii)  
1. Introduction to Quantitative Biology (pg. 1)  
1.1 History and Overview of the qbio Summer School (pg. 1)  
1.2 Origin and Organization of this Textbook (pg. 2)  
1.3 How to Use this Book (pg. 4)  
1.4 Acknowledgments (pg. 6)  
2. Fostering Collaborations between Experimentalists and Modelers (pg. 9)  
2.1 Education (pg. 10)  
2.2 Presentation (pg. 10)  
2.3 Practice (pg. 11)  
2.4 Attitude (pg. 11)  
I. Defining and Simulating Models (pg. 13)  
Introduction to the Simulation of Models (pg. 15)  
3. Modeling with Ordinary Differential Equations (pg. 19)  
3.1 Introduction (pg. 19)  
3.2 A Primer to Ordinary Differential Equations (pg. 20)  
3.3 From Biochemical Reactions Networks to ODEs (pg. 21)  
3.4 Solving ODEs (pg. 27)  
3.5 Complex Dynamic Behavior: Different Types of Solutions (pg. 33)  
3.6 Detailed Balance: Thermodynamic Constraints (pg. 36)  
3.7 Model Simplifications and Level of Abstraction (pg. 38)  
3.8 Some Advanced Modeling Concepts (pg. 42)  
3.9 Overview of Relevant Software Tools (pg. 45)  
3.10 Exercises (pg. 46)  
4. Modeling with Partial Differential Equations (pg. 49)  
4.1 Introduction to Partial Differential Equations (pg. 49)  
4.2 PDE Theory (pg. 56)  
4.3 Analytical Solutions (pg. 57)  
4.4 Numerical Solutions (pg. 63)  
4.5 Summary and Discussion (pg. 66)  
4.6 Exercises (pg. 66)  
5. Stochasticity or Noise in Biochemical Reactions (pg. 71)  
5.1 Introduction (pg. 71)  
5.2 The Chemical Master Equation (pg. 73)  
5.3 Analyzing Population Statistics with FSP Approaches (pg. 77)  
5.4 Comparing CME Models to SingleCell Data (pg. 83)  
5.5 Examples (pg. 85)  
5.6 Summary (pg. 91)  
5.7 Exercises (pg. 92)  
6. The LinearNoise Approximation and Moment Closure Approximations for Stochastic Chemical Kinetics (pg. 95)  
6.1 Introduction (pg. 95)  
6.2 Stochastic Models of Biochemical Systems (pg. 96)  
6.3 Time Evolution of Statistical Moments (pg. 98)  
6.4 Moment Closure Methods (pg. 101)  
6.5 The LinearNoise Approximation (pg. 105)  
6.6 Conclusion (pg. 111)  
6.7 Exercises (pg. 112)  
7. Kinetic Monte Carlo Analyses of Discrete Biomolecular Events (pg. 113)  
7.1 Introduction to Stochastic Simulations (pg. 113)  
7.2 Example (pg. 127)  
7.3 Model Specification Using Petri Nets (pg. 128)  
7.4 bioPN (pg. 131)  
7.5 Exercises (pg. 135)  
8. The Extra Reaction Algorithm for Stochastic Simulation of Biochemical Reaction Systems in Fluctuating Environments (pg. 137)  
8.1 Introduction (pg. 137)  
8.2 The Extrande Method (pg. 138)  
8.3 Gene Expression with TimeVarying Transcription (pg. 142)  
8.4 Discussion (pg. 145)  
9. SpatialStochastic Simulation of ReactionDiffusion Systems (pg. 149)  
9.1 Why Spatiality Matters (pg. 150)  
9.2 Brownian Dynamics Simulations with Reactions (pg. 152)  
9.3 EventDriven Schemes (pg. 161)  
9.4 Recent Developments: Hybrid Schemes and Parallelization (pg. 172)  
9.5 Further Reading (pg. 173)  
9.6 Online Resources (pg. 173)  
9.7 Summary (pg. 174)  
9.8 Exercises (pg. 174)  
10. Introduction to Molecular Simulation (pg. 179)  
10.1 Introduction (pg. 179)  
10.2 Molecular Dynamics (pg. 180)  
10.3 Monte Carlo Sampling (pg. 185)  
10.4 Practical Aspects of Numerical Simulations (pg. 187)  
10.5 Acceleration of Equilibration and Simulating Rare Events (pg. 195)  
10.6 Simulation Tools (pg. 199)  
10.7 Summary (pg. 202)  
10.8 Exercises (pg. 203)  
II. Model Development and Analysis Tools (pg. 207)  
Introduction to Model Development and Analysis (pg. 209)  
11. ReverseEngineering Biological Networks from Large Data Sets (pg. 213)  
11.1 Lay of the Land (pg. 213)  
11.2 Roles for ReverseEngineering in Systems Biology Research (pg. 220)  
11.3 Two Different Meanings of Phenomenological "Reconstruction'' (pg. 228)  
11.4 Discussion (pg. 241)  
11.5 Try on Your Own: Become a Reverse Engineer (pg. 244)  
11.6 Exercises (pg. 245)  
12. Mathematically Controlled Comparisons for Elucidation of Biological Design Principles (pg. 247)  
12.1 Introduction (pg. 248)  
12.2 EndProduct Inhibition: SteadyState Behavior (pg. 251)  
12.3 Transcriptional Autorepression: Dynamic Behavior (pg. 259)  
12.4 Discussion (pg. 265)  
12.5 Summary (pg. 268)  
12.6 Exercises (pg. 269)  
13. Parameter Estimation, Sloppiness, and Model Identifiability (pg. 271)  
13.1 Introduction (pg. 272)  
13.2 Formulating the Parameter Estimation Problem (pg. 273)  
13.3 Solving the Inverse Problem: Nonlinear Optimization (pg. 277)  
13.4 Model Identifiability: Parameters Cannot Always Be Estimated (pg. 279)  
13.5 Precision of Parameter Estimates Using Sensitivity Analysis (pg. 283)  
13.6 Parameter Estimation in the Wild: Practicalities (pg. 289)  
13.7 Summary (pg. 290)  
13.8 Exercises (pg. 290)  
14. Sensitivity Analysis (pg. 293)  
14.1 Introduction (pg. 293)  
14.2 Theoretical Concepts (pg. 294)  
14.3 Applications of the Sensitivity Analysis (pg. 305)  
14.4 Summary (pg. 315)  
14.5 Exercises (pg. 316)  
15. Experimental Design (pg. 321)  
15.1 Introduction (pg. 321)  
15.2 General Framework (pg. 322)  
15.3 Frequentist Approach (pg. 323)  
15.4 Bayesian Approach (pg. 326)  
15.5 Asymptotic Equivalency (pg. 327)  
15.6 Applications of Experiment Design (pg. 328)  
15.7 Discussion (pg. 334)  
15.8 Exercises (pg. 335)  
16. Bayesian Parameter Estimation and Markov Chain Monte Carlo (pg. 339)  
16.1 Introduction (pg. 339)  
16.2 LikelihoodBased Inference (pg. 340)  
16.3 Bayesian Inference (pg. 343)  
16.4 Markov Chain Monte Carlo for Bayesian Inference (pg. 345)  
16.5 LikelihoodFree Methods for Bayesian Inference (pg. 350)  
16.6 Exercises (pg. 355)  
17. Uses of Bifurcation Analysis in Understanding Cellular DecisionMaking Dongya Jia, Mohit Kumar Jolly, and Herbert Levine (pg. 357)  
17.1 Introduction (pg. 357)  
17.2 Basic Concepts in Bifurcation Analysis (pg. 360)  
17.3 Bifurcations in One Dimension (pg. 363)  
17.4 Using Bifurcation Theory to Understand Cellular DecisionMaking (pg. 365)  
17.5 Bifurcation Theory in Parameter Sensitivity Analyses (pg. 375)  
17.6 Bifurcation Theory and Experimental Testing with Flow Cytometry (pg. 377)  
17.7 Conclusions (pg. 377)  
17.8 Exercises (pg. 378)  
18. Performance Measures for Stochastic Processes and the MatrixAnalytic Approach (pg. 379)  
18.1 Introduction (pg. 379)  
18.2 Analysis of the Stochastic Descriptors: An Application to VEGFR2/VEGFA Interaction and Signaling (pg. 382)  
18.3 Numerical Results (pg. 392)  
18.4 Discussion (pg. 394)  
III. Modeling in Practice (pg. 401)  
Introduction to Computational Modeling Tools in Quantitative Biology (pg. 403)  
19. Setting Up and Simulating ODE Models (pg. 405)  
19.1 Introduction to Tellurium: A PythonBased Platform (pg. 405)  
19.2 Building and Simulating a Model (pg. 406)  
19.3 Antimony: Network Description Language (pg. 409)  
19.4 Running Simulations (pg. 411)  
19.5 Fitting Models to Data (pg. 413)  
19.6 Validation, Validation, and More Validation (pg. 416)  
19.7 Publishing a Reproducible Model (pg. 418)  
19.8 Illustrative Examples (pg. 420)  
19.9 Summary (pg. 421)  
19.10 Availability of Software (pg. 421)  
19.11 Exercises (pg. 421)  
20. Accelerating Stochastic Simulations Using Graphics Processing Units (pg. 423)  
20.1 Introduction (pg. 423)  
20.2 Methods (pg. 426)  
20.3 Example (pg. 437)  
20.4 Discussion (pg. 440)  
21. RuleBased Modeling Using Virtual Cell (VCELL) (pg. 441)  
21.1 Introduction (pg. 441)  
21.2 RuleBased Modeling in VCell (pg. 444)  
21.3 Physiology (pg. 445)  
21.4 RuleBased Modeling in VCell: Applications and Simulations (pg. 451)  
21.5 Conclusions (pg. 453)  
21.6 Additional Information (pg. 454)  
22. Spatial Modeling of Cellular Systems with VCELL (pg. 455)  
22.1 Introduction (pg. 455)  
22.2 Compartmental Models: Sizes of Cellular Compartments May Matter even if Diffusion is Fast on the Time Scale of Reactions (pg. 456)  
22.3 ReactionDiffusion in Explicit Geometries: Why Space Should Be Explicitly Modeled (pg. 459)  
22.4 Numerical Approaches to Spatial Models Arising in Cell Biology (pg. 462)  
22.5 Conclusion (pg. 468)  
23. Stochastic Simulation of WellMixed and Spatially Inhomogeneous Biochemical Systems (pg. 469)  
23.1 Introduction (pg. 469)  
23.2 Algorithms (pg. 471)  
23.3 Software for Stochastic Simulation of Biochemical Systems (pg. 474)  
23.4 Examples (pg. 477)  
23.5 Discussion (pg. 480)  
23.6 Summary (pg. 483)  
23.7 Exercises (pg. 483)  
24. Spatial Stochastic Modeling with MCell and CellBlender (pg. 485)  
24.1 Introduction: Why Stochastic Spatial Modeling? (pg. 485)  
24.2 A Brief Overview of MCell (pg. 488)  
24.3 Getting Started with CellBlender and MCell (pg. 493)  
24.4 Simulating Free Molecular Diffusion (pg. 495)  
24.5 Restricting Diffusion by Defining Meshes (pg. 497)  
24.6 Simulating Bimolecular Reactions in a Volume (pg. 499)  
24.7 Simulating Molecules and Reactions on Surfaces (pg. 504)  
24.8 Extended Exercise: A DensityDependent Switch (pg. 509)  
24.9 Concluding Remarks (pg. 511)  
IV. Example Models and Specialized Methods (pg. 513)  
Introduction to Examples in Quantitative Biology (pg. 515)  
25. The Use of Linear Analysis and Sensitivity Functions in Exploring TradeOffs in Biology: Applications to Glycolytic Oscillations (pg. 519)  
25.1 Introduction (pg. 519)  
25.2 Analysis of the Minimal Model of Glycolysis (pg. 524)  
25.3 Discussion (pg. 528)  
26. Models of Bacterial Chemotaxis (pg. 531)  
26.1 Introduction: The E. coli Chemotaxis Network (pg. 531)  
26.2 IsingType Description of the E. coli Chemotactic Process (pg. 536)  
26.3 Summary (pg. 544)  
27. Modeling Viral Dynamics (pg. 545)  
27.1 Introduction: Basic Biology of HIV Infection (pg. 546)  
27.2 A Simple Model of HIV Dynamics (pg. 547)  
27.3 Basic Principles of Viral Dynamics and Drug Treatment (pg. 549)  
27.4 Using Modeling to Gain Further Insight into HIV1 Biology (pg. 551)  
27.5 Other Model Applications and Extensions (pg. 557)  
27.6 Further Reading (pg. 561)  
27.7 Exercises (pg. 561)  
28. Stochastic Modeling of Gene Expression, Protein Modification, and Polymerization (pg. 563)  
28.1 Introduction (pg. 563)  
28.2 Gene Expression (pg. 564)  
28.3 Protein Modification (pg. 572)  
28.4 Polymerization (pg. 574)  
28.5 Interactions (pg. 577)  
28.6 More Complex Phenomena (pg. 579)  
28.7 Summary and Outlook (pg. 580)  
28.8 Exercises (pg. 580)  
29. Modeling CellFate Decisions in Biological Systems: Bacteriophage, Hematopoietic Stem Cells, EpithelialtoMesenchymal Transition, and Beyond (pg. 583)  
29.1 Introduction (pg. 583)  
29.2 Lysis/Lysogeny Decision in Lambda Phage (pg. 585)  
29.3 CellFate Decisions in Hematopoietic Stem Cell System (pg. 588)  
29.4 EpithelialtoMesenchymal Transition (pg. 590)  
29.5 NotchDeltaJagged Signaling (pg. 594)  
29.6 Which Modeling Framework to Use and When? (pg. 597)  
29.7 Exercises (pg. 598)  
30. Tutorial on the Identification of Gene Regulation Models from SingleCell Data (pg. 599)  
30.1 Outline of Our Approach (pg. 599)  
30.2 Gene Regulation Model Description (pg. 600)  
30.3 Exercise Tasks (pg. 603)  
30.4 Exercise Results and GUI (pg. 614)  
30.5 Summary and Conclusions (pg. 616)  
References (pg. 617)  
Contributors (pg. 695)  
Index (pg. 701) 
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